What is not changed when work is done by a machine?
2 answers:
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a) 0 kg m/s
b) 0 kg m/s
c) +3 m/s
d) 60 N
Explanation:
a)
The momentum of an object is a vector quantity given by:
where
m is the mass of the object
v is the velocity of the object
In this problem, we have a system of two people, so the total momentum will be the sum of the individual momenta of the two people:
Which can be rewritten as
where are the masses of the two people and
their initial velocities.
However, the two people are initially at rest, so
Therefore the total momentum is
b)
The principle of conservation of momentum states that when there are no external forces acting on a system, the total momentum of the system is conserved, so we can write:
where
is the total momentum of the system before
is the total momentum of the system after
In this problem,
As we calculated in part a: this is because the total momentum of the two people before they push off each other is zero.
Therefore, according to the law of conservation of momentum,
So the total momentum is zero also after they push off each other.
c)
The total momentum of the girl and the boy after they push off each other can be written as:
(1)
where:
is the mass of the girl
is her velocity (she moves backward, so the negative sign)
is the mass of the boy
is the velocity of the boy
As calculated in part b), we also know that the total momentum of the girl and the boy is
(2)
By combining eq(1) and eq(2) we get
And solving for v2 we find the velocity of the boy:
and the positive sign means he is moving forward.
d)
We can solve this part by applying the impulse theorem, which states that the change in momentum of an object is equal to the product between the force applied on it and the duration of the collision:
where
is the change in momentum
F is the force
is the time during which the force is applied
In this problem:
For the boy, the change in momentum is:
And since
We have
So, the force exerted between the boy and the girl is: